Thermal Expansion: Definition, Equation & Examples

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  • 0:00 What is Thermal Expansion?
  • 1:05 Equation
  • 1:35 Example
  • 3:00 Lesson Summary
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Lesson Transcript
David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Expert Contributor
Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

In this lesson, you will learn what thermal expansion is and discover an equation for calculating how much different materials expand. You'll look at a number of examples of thermal expansion. A short quiz will follow.

What is Thermal Expansion?

One day you're trying to open a pickle jar, but the lid is super tight and you just can't do it. You try using a rubber grip, but that doesn't work. You try hitting the jar lid on the counter to break the seal, but nothing happens. Finally, you try your grandma's favorite trick: you run the metal jar lid under hot water to heat it up. The jar opens easily. But why? The answer is thermal expansion.

Thermal expansion occurs when an object expands and becomes larger due to a change in the object's temperature. To understand how this happens, we need to think about what temperature actually is. Temperature is the average kinetic (or movement) energy of the molecules in a substance. A higher temperature means that the molecules are moving faster on average. If you heat up a material, the molecules move faster and, as a result, they take up more space - they tend to move into areas that were previously empty. This causes the size of the object to increase.

So when you heat up the jar lid, the same thing happens - the jar lid expands. So does the glass, but metals expand more than glass. The gaps between the metal jar lid and the glass threads increase, so it becomes easier to open.


This equation describes a linear thermal expansion, which we'll examine in the context of a metal bar expanding and increasing its length:

Equation of Linear Expansion

In this equation, delta L is the change in length of the bar, delta T is the change in temperature of the bar, L is the original length before the temperature changed, and alpha is the linear coefficient of thermal expansion. The coefficient is just a number that represents how much the material expands. Metals, for example, tend to expand more than plastics.


We've already talked about opening a stubborn jar, but another example of thermal expansion is the joints of a bridge. Bridges are built out of concrete and other relatively firm materials, but these materials expand just like anything else. When that happens, a bridge could break and collapse. To avoid this, expansion joints are placed on large bridges. That way, as the temperature varies over the course of the year, the bridge is free to get longer or shorter, without causing cracks or breakages.

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Thermal Expansion

According to the molecular theory of matter, objects absorbing thermal energy have molecules with increasing kinetic energy. This causes the object to expand. All three states of matter undergo thermal expansion. Solids expand in a linear fashion, in an areal fashion (superficial), and in a volumetric (cubical) fashion. Liquids and gases undergo only volumetric expansion. The equations for these thermal expansions are listed below.

Phase of MatterType of ExpansionEquation
SolidLinearΔL= L0 α Δ T
SolidArealΔA = A0 2α Δ T
SolidVolumetricΔV = V0 3α Δ T
LiquidVolumetricΔV = V0 β Δ
GasVolumetricPV = nRT
  • Δ L, Δ A; Δ V represent the change in length, area, and volume, respectively
  • α and β are coefficients of expansion
  • L represents length
  • Δ T represents change in temperature
  • n represents moles of gas
  • R represents the ideal gas constant

Let's practice answering a few questions regarding thermal expansion.


  1. Imagine a metallic object has an α value of 12 x 10-6 / ° C. Its initial length is 40 meters long and its temperature increased by 100° C. Which equation would you use to determine the object's new length?
  2. What is the new length of the object from question 1?
  3. What phase of matter requires the mass of the object to determine its volume?
  4. Based on what you know of linear expansion, why do you think poured concrete has joints in it?


  1. ΔL= L0 α Δ T
  2. ΔL= (50 m)(12 x 10-6 / °C)(100° C) = 0.06 m, which is the change in length that we add to the original length of 50 m giving us 50.06 m, or 50 m and 6 cm.
  3. Gas
  4. Joints in poured concrete allow the concrete to expand and contract due to heating/cooling, thus preventing the concrete from cracking.

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